CN116294811A - Armed helicopter fire flight cooperative mechanism analysis method based on multi-target wolf swarm algorithm - Google Patents

Armed helicopter fire flight cooperative mechanism analysis method based on multi-target wolf swarm algorithm Download PDF

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CN116294811A
CN116294811A CN202310130591.3A CN202310130591A CN116294811A CN 116294811 A CN116294811 A CN 116294811A CN 202310130591 A CN202310130591 A CN 202310130591A CN 116294811 A CN116294811 A CN 116294811A
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王玉惠
庞东
陈谋
郭钟格
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a method for analyzing a fire flight cooperative mechanism of an armed helicopter based on a multi-target wolf swarm algorithm. The method aims at the problem of aiming attack of the air to the ground target of the rotary turret class weapons such as the armed helicopter air cannon, and mainly establishes an aiming attack mechanism of the air to the ground of the rotary turret class weapons through an improved CCIP rotary turret class fire control calculation method and a multi-target optimization method. Firstly, according to the aiming mode and characteristics of a weapon of a turning turret class of an armed helicopter, the original CCIP fire control calculation method is analyzed and improved, and a novel IFFC coupler is provided to solve the problem of cooperative attack between the armed helicopter and a weapon follow-up system; secondly, a multi-objective function optimization model for aiming the turning turret class weapon of the armed helicopter is established through angle error analysis and dynamic coupling analysis; and finally solving the optimization problem by an improved multi-target self-adaptive wolf-swarm method, and verifying the feasibility and effectiveness of the method by simulation.

Description

Armed helicopter fire flight cooperative mechanism analysis method based on multi-target wolf swarm algorithm
Technical Field
The invention belongs to the technical field of target aiming of armed helicopters, and particularly relates to a method for analyzing a fire flight coordination mechanism of an armed helicopter based on a multi-target wolf algorithm.
Background
Due to the rapid development of flight control technology and airborne weapon technology, armed helicopters with high maneuverability play an increasingly important role in the modern battlefield of transient variation, particularly low-altitude ground attack tasks. In the ground attack process, compared with a hanger weapon, the weapon line driving method has the advantage that the weapon line is driven by controlling the weapon follow-up system, and the capability of the weapon line to rapidly rotate in the transverse and longitudinal directions greatly improves the attack and the survivability of the armed helicopter in a low-altitude complex environment. For high-altitude fighter types such as fighter plane and bomber, the control weapon follow-up system drives a weapon line which is one of the short-distance defense means, but is a main attack means for the armed helicopter for ultra-low-altitude fighter, so that the research on the high-precision and high-efficiency weapon follow-up system is very critical for improving the accurate attack level of rotating gun towers such as the armed helicopter cannon.
Based on the IFFC system, the armed helicopter mostly adopts GG aiming principle to perform fire control calculation on the weapon follow-up system air-to-ground aiming attack problem, and has the advantages that the flight attitude of the armed helicopter is not required to be adjusted in the aiming process, and the target aiming is performed only by operating the rotary turret, so that the method meets the original purpose of designing the rotary turret weapons. Its advantages are high flying freedom and high pilot's operability. However, with the progress of computer technology, the on-board weapon system starts to develop towards the direction of systemization, intellectualization and automation, and the traditional principle of aiming the armed helicopter with a rotating turret like GG does not have the effect of adjusting the posture of the armed helicopter on the rotation of a weapon follow-up system, so that the aiming efficiency is greatly dependent on the driving of a pilot and the proficiency of aiming a target, which is contrary to the development of the intellectualization and automation of the weapon system.
Therefore, we no longer consider the armed helicopter and weapon follow-up system as two independent systems, but consider the effect of the attitude of the armed helicopter on the weapon line being maneuvered by the weapon follow-up system while simultaneously taking it into account the altitude and azimuth of the weapon line. Therefore, the original CCIP aiming principle is improved, and the mutual coupling relation and the adjustment mechanism of two systems in the aiming process are considered, so that an air-to-ground aiming mechanism which is more in line with the actual turning turret type weapon of the armed helicopter is established.
In summary, in order to ensure the accuracy and rapidity of the armed helicopter in the process of attacking the ground through the aerial cannon, the problem of target aiming attack of the rotating turret weapon such as the armed helicopter aerial cannon should be continuously studied.
Disclosure of Invention
For the problem of ground-to-air attacks of armed helicopters in actual battlefields, integrated fire/flight control (IFFC) systems aim to integrate the fire control system and the flight control system into one system through a fire/flight coupler. However, conventional IFFC systems fail to achieve high accuracy targeting when armed helicopters attack targets using an armed follower system. Firstly, on the basis of analyzing the CCIP aiming principle of the armed helicopter, a novel IFFC coupler is provided to solve the problem of cooperative attack between the armed helicopter and a weapon follow-up system. Second, in the new IFFC coupler, the aiming problem is converted into a multi-objective optimization problem using angular error analysis and dynamic coupling analysis. Finally, to solve this problem, an improved adaptive multi-objective wolf's method (AMOWA) was devised and its effectiveness was demonstrated by simulation.
The invention adopts the following technical scheme for solving the technical problems:
the armed helicopter fire flight cooperative mechanism analysis method based on the multi-target wolf swarm algorithm comprises the following steps:
step 1), establishing a CCIP fire control calculation vector relation of the armed helicopter rotating turret weapons, and acquiring projectile hit point pitch angle, hit point azimuth angle and projectile flight time information of the armed helicopter rotating turret weapons;
step 2) converting a target angle aiming problem into a multi-target optimization problem by utilizing target aiming angle error analysis and dynamic coupling analysis;
and 3) designing a multi-objective wolf swarm algorithm, and solving the multi-objective optimization problem in the step 2).
Preferably, in step 1): the CCIP fire control calculation vector relation of the armed helicopter rotating turret weapon is as follows:
Figure BDA0004083652490000021
wherein,,
Figure BDA0004083652490000022
for the target speed vector, +.>
Figure BDA0004083652490000023
For wind speed vector>
Figure BDA0004083652490000024
Is a comprehensive wind speed vector; t (T) d In order to achieve a time of flight of the projectile,
Figure BDA0004083652490000025
mounting a potential difference vector for a rotary turret type weapon; />
Figure BDA0004083652490000026
Is the distance vector from the shot point to the shot drop point, +.>
Figure BDA0004083652490000027
Is a pellet ray vector>
Figure BDA0004083652490000028
A ballistic reduction vector for the projectile;
the vector equation in the formula (1) is projected to the machine body coordinate system in a triaxial way to obtain:
Figure BDA0004083652490000031
wherein [ A ] x A y A z ]Is a distance vector
Figure BDA0004083652490000032
Components projected onto the machine body coordinate system in three axes [ U ] zx U zy U zz ]For the integrated wind speed vector->
Figure BDA0004083652490000033
Components of three-axis projection to body coordinate system, V 1 To the absolute velocity of the projectile, V 0 Airspeed, V, of armed helicopters 01 V is the relative velocity of the projectile w Mu, azimuth of weapon line w The angle is the weapon line height angle, alpha is the transverse entering angle of the armed helicopter, and beta is the longitudinal entering angle of the armed helicopter; phi is the yaw angle of the armed helicopter, theta is the pitch angle of the armed helicopter, and phi is the roll angle of the armed helicopter;
according to (2), the pitch angle mu of the impact point of the projectile c Azimuth v of hit point c And the shot flight time T d The expressions of (2) are respectively:
Figure BDA0004083652490000034
Figure BDA0004083652490000035
Figure BDA0004083652490000036
wherein V is pj Is the average speed of the projectile.
Preferably, the implementation process of step 2) is as follows:
step 2.1) target aiming angle error analysis:
as is known from (2) - (5), the hit point pitch angle μ c Azimuth v of hit point c Time of flight T of projectile d Yaw angle phi, pitch angle theta, roll angle phi and weapon line height angle mu of armed helicopter w Azimuth v of weapon line w There is a functional relationship:
Figure BDA0004083652490000041
let the target line have a high-low angle mu c c Target line azimuth v c c Then the target aiming angle error equation of the IFFC fire and flight system of the armed helicopter is:
Figure BDA0004083652490000042
wherein N is μ For the error between the high and low angles of the weapon line and the target line, N ν Error of weapon line azimuth and target line azimuth;
to achieve air-to-ground aiming, N μ And N ν Satisfy formula (8):
Figure BDA0004083652490000043
solving (8) to obtain the attitude instruction phi of the armed helicopter in the IFFC fire and flight system c 、θ c 、ψ c And weapon follow-up system command mu w c 、ν w c ；
Let Φ= [ Φθψμ ] w ν w ] T As a parameter vector, a target aiming angle error optimization function is defined:
F 1 (Φ)＝N μ 2 (Φ)+N ν 2 (Φ) (9)
step 2.2) dynamic coupling analysis of target aiming angle errors
IFFC fire and flight systems are divided into two direct coupling channels: { mu c ,μ w θ and { v }, respectively c ,ν w Phi, the rest channels are indirect coupling channels;
through the high and low angles of the target line
Figure BDA0004083652490000045
And target azimuth>
Figure BDA0004083652490000046
For the hit point pitch angle mu c Azimuth v of hit point c And (5) deriving to obtain:
Figure BDA0004083652490000044
on the basis of equation (10), a dynamic coupling matrix G is defined:
Figure BDA0004083652490000051
to determine the effect of an indirect coupling channel on a direct coupling channel, a dynamic coupling function is defined as:
Figure BDA0004083652490000052
based on the formula (12), establishing a coupling influence degree optimization function:
F 2 (Φ)＝K 1 (Φ)+K 2 (Φ) (13)
step 2.3) defining a Multi-objective function optimization model
Defining an air-to-ground aiming multi-target optimization model of a turning turret type weapon of an armed helicopter as follows:
Figure BDA0004083652490000053
wherein phi is max For maximum yaw angle, θ max Is the maximum pitch angle, ψ max At maximum roll angle, mu wmax1 Sum mu wmax2 V is the angle of the maximum weapon line wmax Is the maximum weapon line azimuth.
Preferably, the implementation process of step 3) is as follows:
step 3.1), the Pareto principle is adopted to measure the solution in the air-to-ground aiming multi-target optimization model of the turning turret weapons of the armed helicopter;
establishing a feasible domain:
Figure BDA0004083652490000054
based on the concept of Pareto optimal solution, the Pareto optimal solution set of the air-to-ground aiming multi-target optimization model of the turning turret type weapon of the armed helicopter is as follows:
Figure BDA0004083652490000061
wherein, the individual solves phi a And phi is b The method comprises the following steps of:
Φ a ＝[φ a ,θ a ,ψ a ,μ wa ,ν wa ] T ∈Ω (17)
Φ b ＝[φ b ,θ b ,ψ b ,μ wb ,ν wb ] T ∈Ω (18)
wherein a and b are parameters;
step 3.2) designing a self-adaptive crowding wolf group individual selection criterion;
the degree of congestion is defined as formula (19):
Figure BDA0004083652490000062
wherein, the individual solves phi i ＝[φ i ,θ i ,ψ i ,μ wi ,ν wi ] T E ρ, i is a parameter, D c (Φ i ) To solve phi for individuals i Degree of congestion, phi i-1 And phi is i+1 Is equal to phi i Adjacent two individual solutions, F m (Φ i+1 ) And F m (Φ i-1 ) To solve phi for individuals i+1 And phi is i+1 The function value of the corresponding mth objective function; f (F) m (Φ max ) And F m (Φ min ) The mth objective function in the Pareto optimal solution setMaximum and minimum values;
design adaptive congestion degree V (phi) i,t ) As in formula (20):
Figure BDA0004083652490000063
wherein e is an exponential function, t is the iteration number, D c (Φ i,t ) Is the crowding degree, k of the ith individual in the t-th iteration process 1 And k 2 Is an adaptive scaling factor;
design the selection criteria of the wolf and the wolf to be detected:
solving the phi of individual i The definition is as follows:
Figure BDA0004083652490000064
wherein N is w The number of individuals is the number of wolves;
determining the number of individuals of the wolves through the Pareto optimal solution set, and after determining the number of individuals of the wolves, determining the number of the individuals of the Pareto optimal solution set as the probability of being selected as the wolves by using a roulette method is expressed as follows:
Figure BDA0004083652490000071
wherein j is a parameter;
the self-adaptive search direction and step size of the wolf are designed, expressed as:
Figure BDA0004083652490000072
wherein,,
Figure BDA0004083652490000073
for the position of the ith wolf in the d dimension at the t iteration,/th>
Figure BDA0004083652490000074
For the position of the first wolf in the d-th dimension at the t-th iteration, ++>
Figure BDA0004083652490000075
Representing the slash wolf and the head wolf +.>
Figure BDA0004083652490000076
The distance between the two is an exponential function, e is an exponential function, lambda is a logarithmic spiral constant, l 1 Is [ -1,1]Random numbers, k uniformly distributed in interval 3 And k 4 A, b are parameters, which are self-adaptive proportionality coefficients;
the other individual solutions except for the head wolves and the slash wolves are determined as the exploring wolves, and the number of the exploring wolves is S _num The method comprises the steps of carrying out a first treatment on the surface of the The iteration step length and direction of the detection wolf are designed as follows:
Figure BDA0004083652490000077
wherein,,
Figure BDA0004083652490000078
for the j-th detection wolf at the position of the d-th dimension at the t-th iteration,/the position of the j-th detection wolf at the d-th dimension at the t-th iteration>
Figure BDA0004083652490000079
Is the direction of the iteration and,
Figure BDA00040836524900000710
is the iteration step length, h d Is the number of directions, parameter p d Has a value of 1 to h d ，l 2 Is [0.5,1.5]Random numbers uniformly distributed in the interval;
the implementation process of the multi-target wolf's group algorithm is as follows:
step1: to individual solve phi i Number of individuals N of wolves w Initializing and setting the maximum iteration times t max ；
step2, calculating objective function values of all wolf individuals and determining a Pareto solution set through a Pareto dominance relation;
step3: selecting primary first-generation wolf individuals with the position phi according to the Pareto optimal solution set established by the formula (16) and the definition of the adaptive crowding degree in the formula (20) lead The method comprises the steps of carrying out a first treatment on the surface of the The rest individuals in the Pareto optimal solution set select the wolf individuals through a formula (22), and the wolf individuals perform the running behavior through a formula (23); meanwhile, determining a wolf probing individual outside the Pareto optimal solution set, wherein the wolf probing individual walks through a formula (24); when individuals superior to the first wolf are generated in the first wolf individuals and the second wolf individuals, the next step is performed;
step4: updating the Pareto optimal solution set, judging whether the Pareto solution set in step2 reaches an upper limit, if so, eliminating individuals with high crowding degree and carrying out the next step, otherwise, directly carrying out the next step;
step5: judging whether the maximum iteration times t are reached max And outputting all non-inferior solutions in the Pareto solution set in step2 if the solution is reached, otherwise, turning to step2.
The beneficial effects of the invention are as follows:
1. and the fire-fly coupler is designed based on the angle error, so that the coupling and cooperative relationship between the attitude angle of the armed helicopter and the rotation angle of the weapon follow-up system can be analyzed conveniently, and an efficient cooperative mechanism is obtained.
2. The multi-target optimization model of the armed helicopter aiming at the ground is established and calculated by a self-adaptive multi-target wolf group method, so that more flight aiming influence factors can be considered in the aiming process of aiming at the ground, and the method is more suitable for the actual aiming attack of the armed helicopter.
Drawings
FIG. 1 is a basic block diagram of an IFFC of an armed helicopter of the invention;
FIG. 2 is a diagram of a CCIP fire control calculation vector for a turret class weapon rotated by an armed helicopter in accordance with the present invention;
FIG. 3 is a flow chart of the adaptive multi-objective wolf-shoal method of the present invention;
FIG. 4 is a simulation diagram of an optimal solution set for aiming optimization functions of an armed helicopter of the present invention.
Detailed Description
1 rotating turret class weapon IFFC fire control solution
Different from the hanger type weapon, the weapon line adjustment is directly realized by adjusting the attitude angle of the armed helicopter, and the rotation turret type weapon needs to consider the cooperative coordination between the two systems of the armed helicopter and the weapon follow-up system to finally realize aiming, so that subsystems such as the original armed helicopter system, the target motion state, the fire control system and the like also need to be considered, and the weapon follow-up system and a weapon follow-up system controller are also needed. In an armed helicopter rotary turret weapon IFFC system, the basic aiming attack implementation of an armed helicopter rotary turret weapon is shown in fig. 1.
According to the principle of the air-to-ground CCIP of the armed helicopter, a CCIP fire control calculation vector diagram of the rotating turret weapon of the armed helicopter is established as shown in fig. 2.
Wherein O-XYZ is a geographic coordinate system, O is the shooting point of the armed helicopter, O' is the projection of O on the ground,
Figure BDA0004083652490000081
airspeed vector for armed helicopter, H is altitude, < +.>
Figure BDA0004083652490000082
For wind speed vector>
Figure BDA0004083652490000083
For the target speed vector, +.>
Figure BDA0004083652490000084
Is the integrated wind velocity vector. />
Figure BDA0004083652490000085
For weapon projectile absolute velocity vector, +.>
Figure BDA0004083652490000086
Is the relative velocity vector of weapon projectile, T d For weapon projectile time of flight, +.>
Figure BDA0004083652490000091
A potential difference vector is installed for the weapon. />
Figure BDA0004083652490000092
For the distance vector from the firing point O of the armed helicopter to the weapon projectile landing point C, +.>
Figure BDA0004083652490000093
For weapon projectile ray vector, +.>
Figure BDA0004083652490000094
A vector for reducing the trajectory of the weapon projectile. As can be seen from fig. 2:
Figure BDA0004083652490000095
the three-axis projection of the vector equation in the formula (1) to the machine body coordinate axis can be obtained:
Figure BDA0004083652490000096
wherein [ A ] x A y A z ]Is that
Figure BDA0004083652490000097
Components projected onto the machine body coordinate system in three axes [ U ] zx U zy U zz ]Is->
Figure BDA0004083652490000098
Components of three-axis projection to body coordinate system, V 1 For absolute velocity of weapon projectile, V 0 Airspeed, V, of armed helicopters 01 V is the relative velocity of the weapon projectile w Mu, azimuth of weapon line w The angle of the weapon line is the transverse entry angle of the armed helicopter, and the angle of the weapon line is the longitudinal entry angle of the armed helicopter. After the projection, the vectors in expression (1) are all changed to the corresponding scalar quantities.
According to (2), the armed helicopter rotates the hit point pitch angle mu of the weapon of the turret class c Azimuth v of hit point c And the shot flight time T d Expression of (2)The formula is:
Figure BDA0004083652490000099
Figure BDA00040836524900000910
Figure BDA00040836524900000911
wherein V is pj Is the average speed of weapon projectile.
2 optimization model of ground attack target of rotary turret weapon based on angle error analysis and coupling error analysis
1) Target aiming angle analysis
In a two-dimensional plane, an air combat target x i Target x for air combat j According to 5 features, define its similarity distance as
As can be seen from (2) - (5), the hit point pitch angle μ c Azimuth v of hit point c Time of flight T of projectile d Yaw angle phi, pitch angle theta, roll angle phi and weapon line height angle mu of armed helicopter w Azimuth v of weapon line w There is a functional relationship of the following formula:
Figure BDA0004083652490000101
let the target line have a high-low angle mu c c Target line azimuth v c c The armed helicopter IFFC system aiming error equation can be expressed as:
Figure BDA0004083652490000102
wherein N is μ For the error between the high and low angles of the weapon line and the target line, N ν Is the weapon line azimuth and target line azimuth error.
To achieve air-to-ground aiming, N μ And N ν The following should be satisfied:
Figure BDA0004083652490000103
the attitude instruction phi of the armed helicopter in the IFFC system can be obtained through the solution formula (8) c 、θ c 、ψ c And weapon follow-up system command signal mu w c 、ν w c . The equation (8) is a complex nonlinear equation set, so that the analytical solution cannot be directly calculated, and the numerical solution is obtained by adopting a numerical optimization method. Let Φ= [ Φθψμ ] w ν w ] T As a parameter vector, an angle error optimization function is defined:
F 1 (Φ)＝N μ 2 (Φ)+N ν 2 (Φ) (9)
2) Target aiming dynamic coupling analysis
From equation (9), it can be seen that the IFFC system of the armed helicopter and its weapon follow-up system is a complex nonlinear system. When aiming at a target through attitude adjustment of the armed helicopter and rotation of the weapon follower system, changes in the attitude of the armed helicopter will affect the weapon follower system rotation, and rotation of the weapon follower system will also affect the attitude adjustment of the armed helicopter. The interaction between the two systems will result in a reduction of the aiming accuracy.
During aiming, the pitch angle of the armed helicopter and the high and low angle of the weapon line of the weapon follow-up system directly influence the elevation angle of the hit point. Similarly, the yaw angle of an armed helicopter and the azimuth angle of the weapon line of the weapon follower system directly affect the azimuth angle of the hit point. Accordingly, IFFC systems may be divided into two direct coupling channels: { mu c ,μ w θ and { v }, respectively c ,ν w Phi }. The other channels are indirect coupling channels.
Based on dynamic coupling analysis mechanism, through
Figure BDA0004083652490000114
And->
Figure BDA0004083652490000115
Deriving the attitude angle of the armed helicopter and the weapon line angle of a weapon follow-up system, and obtaining:
Figure BDA0004083652490000111
based on equation (10), the dynamic coupling matrix G can be described as:
Figure BDA0004083652490000112
to determine the effect of an indirect coupling channel on a direct coupling channel, a dynamic coupling function is defined as
Figure BDA0004083652490000113
Based on the formula (12), establishing a coupling influence degree optimization function:
F 2 (Φ)＝K 1 (Φ)+K 2 (Φ) (13)
3) Multi-objective function optimization model
The air-to-ground aiming multi-target optimization model of the armed helicopter rotating turret weapons is as follows:
Figure BDA0004083652490000121
wherein phi is max For maximum yaw angle, θ max Is the maximum pitch angle, ψ max At maximum roll angle, mu wmax1 Sum mu wmax2 V is the angle of the maximum weapon line wmax Is the maximum weapon line azimuth.
3 air-to-ground target aiming optimization solution based on improved wolf's group method
For the multi-constraint multi-objective optimization problem, in order to make the resulting solution an optimal solution for multiple objective functions, we need to build an optimal solution set to balance the individual objective functions. And the Pareto principle is adopted to measure the merits of the armed helicopter moving turret weapons on solutions in the target aiming optimization model. Establishing a feasible domain:
Figure BDA0004083652490000122
next, pareto dominance is determined. If phi a ＝[φ a ,θ a ,ψ a ,μ wa ,ν wa ] T e.OMEGA.and.phi. b ＝[φ b ,θ b ,ψ b ,μ wb ,ν wb ] T ε Ω satisfies the following formula:
Figure BDA0004083652490000123
phi is a Pareto governs Φ b Marked as phi a ＜Φ b . If they do not constitute a Pareto relationship, they are said to be non-inferior. In the feasible domain, if there is no phi b So that phi is b ＜Φ a Then refer to phi a Is the Pareto optimal solution. Based on the concept of Pareto optimal solution, the Pareto optimal solution set for the multi-objective optimization problem is as follows:
Figure BDA0004083652490000124
the introduction of the Pareto optimal solution set solves the judgment of the merits among objective functions of the multi-objective function optimization problem, but in the iterative process, how to select one solution to become the first wolf becomes an important problem to be solved, and the self-adaptive crowded wolf individual selection criterion is designed according to the method practice on the basis of the traditional crowded concept.
The definition of the degree of congestion is as follows:
Figure BDA0004083652490000131
wherein phi is i ＝[φ i ,θ i ,ψ i ,μ wi ,ν wi ] T ∈ρ，D c (Φ i ) Is phi i Degree of congestion D c The larger the congestion degree is, the smaller the congestion degree is. Phi i-1 And phi is i+1 Is equal to phi i Adjacent two solutions, F m (Φ i+1 ) And F m (Φ i-1 ) The function value of the mth objective function corresponding to the function value. F (F) m (Φ max ) And F m (Φ min ) Maximum and minimum values of the mth objective function in the Pareto optimal solution set.
When the head wolves are selected through the crowding degree, the individuals with large crowding degree are usually selected to be the head wolves, so that the convergence of the whole method is facilitated, and meanwhile, the method is easy to sink into local optimum due to the selection mode; conversely, if an individual with a small degree of congestion is selected, the rapidity and convergence of the method are seriously affected. Therefore, on the basis of the original crowding definition, an adaptive crowding concept is designed:
Figure BDA0004083652490000132
wherein t is the iteration number of the method, D c (Φ i,t ) Is the crowding degree, k of the ith individual in the t-th iteration process 1 And k 2 Is an adaptive scaling factor.
After determining the selection criteria of the first wolf, the selection criteria of the first wolf and the second wolf are analyzed, as well as their search steps and directions. For ease of analysis and description, the individual solutions Φ i The definition is as follows:
Figure BDA0004083652490000133
wherein N is w Is the number of individuals in the wolf group.
The wolf is first selected. The individual of the wolf is determined by Pareto optimal solution set. After the number of individuals is determined, the roulette method is used to determine the wolves. The probability that an individual in the Pareto optimal solution set is selected as a wolf can be expressed as
Figure BDA0004083652490000134
In order to improve the optimization quality, the self-adaptive search direction and step length of the wolves are designed by referring to a whale optimization method, and can be expressed as follows:
Figure BDA0004083652490000135
wherein,,
Figure BDA0004083652490000141
for the position of the ith wolf in the d dimension at the t iteration,/th>
Figure BDA0004083652490000142
For the position of the first wolf in the d-th dimension at the t-th iteration, ++>
Figure BDA0004083652490000143
Representing the individual and head wolf of the branchlet under the current iteration number>
Figure BDA0004083652490000144
The distance between the two is an exponential function, e is an exponential function, lambda is a logarithmic spiral constant, l 1 Is [ -1,1]Random numbers, k uniformly distributed in interval 3 And k 4 Is an adaptive scaling factor.
The rest solutions are determined as the exploring wolves except the head wolves and the slash wolves, and the number of the exploring wolves is S _num . The iteration step length and the direction of the detection wolf are designed as
Figure BDA0004083652490000145
Wherein,,
Figure BDA0004083652490000146
for the j-th detection wolf at the position of the d-th dimension at the t-th iteration,/the position of the j-th detection wolf at the d-th dimension at the t-th iteration>
Figure BDA0004083652490000147
Is the direction of the iteration and,
Figure BDA0004083652490000148
is the iteration step. h is a d Is the number of directions, p d Has a value of 1 to h d ，l 2 Is [0.5,1.5]Random numbers uniformly distributed in the interval.
The improved self-adaptive multi-target wolf group method comprises the following basic steps:
step1: for the position phi of the wolf group individual i Number of individuals N of wolves w Initializing and setting the maximum iteration times t max 。
step2, calculating all wolf group individual objective function values and determining a Pareto solution set through a Pareto dominant relationship;
step3: selecting primary first-generation wolf individuals with the position phi according to the Pareto optimal solution set established by the formula (17) and the definition of the adaptive crowding degree in the formula (19) lead . The rest of the individuals in the Pareto optimal solution set select the wolves by the formula (21) and conduct the attack by the formula (22). Meanwhile, the individual wolf probes are determined outside the Pareto optimal solution set, and walk through the formula (23). When individuals superior to the first wolf are generated in the first wolf and the second wolf, the next step is performed;
step4: updating a Pareto optimal solution set, judging whether the solution set reaches an upper limit, if so, removing individuals with large crowding degree through the crowding degree and carrying out the next step, otherwise, directly carrying out the next step;
step5: judging whether the maximum iteration times t are reached max And outputting all non-inferior solutions in the Pareto solution set if the result is reached, otherwise, turning to step2.
The optimization solution flow is shown in fig. 3.
In order to verify the rationality of theory and the effectiveness of the method, a MATLAB platform is utilized for simulation analysis. Setting the initial speed of the armed helicopter to 40m/s and the target movement speed V of the tank x ＝20m/s，V y ＝10m/s，V z =5m/s, weapon projectile initial velocity 500m/s, weapon mounting potential difference 0.1m, wind speed V x ＝3m/s，V y ＝3m/s，V z ＝3m/s，α＝β＝0°，
Figure BDA0004083652490000152
. The initial population size of the method is 300, the maximum non-inferior solution set size is 20, and the maximum iteration number is 200. The Pareto optimal solution set obtained in the scene is shown in fig. 4:
as can be seen from fig. 4, in the case of the target line height angle and the target line azimuth, all the non-inferior solutions finally obtained are linear overall and have a small overall crowding degree, and the angle error function value and the coupling degree function value are all within a small interval. Therefore, the method realizes reasonable adjustment of the hit point high-low angle and the target line azimuth under the conditions of the angle target line high-low angle and the target line azimuth, and finishes the aim attack task while minimizing the coupling influence among all channels.
In fig. 4, the various optimal solution angle error objective function values, coupling error objective function values, and their corresponding armed helicopter and weapon follow-up system signals are shown in the following table:
TABLE 1 optimal solution set function and instruction Signal variable table
Figure BDA0004083652490000151
The armed helicopter attitude command signals and weapon follow-up system command signals corresponding to different non-inferior solutions can be obtained through the table 1. According to analysis, in each adjustment scheme, three attitude command signals of the armed helicopter are in a reasonable range, and the reasonable attitude command signals are critical to the flight safety of the armed helicopter in an actual battlefield, so that the rationality of the method design is also proved.

Claims (4)

1. The armed helicopter fire flight cooperative mechanism analysis method based on the multi-target wolf swarm algorithm is characterized by comprising the following steps of:
step 1), establishing a CCIP fire control calculation vector relation of the armed helicopter rotating turret weapons, and acquiring projectile hit point pitch angle, hit point azimuth angle and projectile flight time information of the armed helicopter rotating turret weapons;
step 2) converting a target angle aiming problem into a multi-target optimization problem by utilizing target aiming angle error analysis and dynamic coupling analysis;
and 3) designing a multi-objective wolf swarm algorithm, and solving the multi-objective optimization problem in the step 2).
2. The method for analyzing the fire flight coordination mechanism of the armed helicopter based on the multi-target wolf algorithm as set forth in claim 1, wherein in the step 1), the following steps are carried out: the CCIP fire control calculation vector relation of the armed helicopter rotating turret weapon is as follows:
Figure FDA0004083652480000011
wherein,,
Figure FDA0004083652480000012
for the target speed vector, +.>
Figure FDA0004083652480000013
For wind speed vector>
Figure FDA0004083652480000014
Is a comprehensive wind speed vector; t (T) d For the time of flight of the projectile, < > is->
Figure FDA0004083652480000015
Mounting head for rotary turret weaponsA vector; />
Figure FDA0004083652480000016
Is the distance vector from the shot point to the shot drop point, +.>
Figure FDA0004083652480000017
Is a pellet ray vector>
Figure FDA0004083652480000018
A ballistic reduction vector for the projectile;
the vector equation in the formula (1) is projected to the machine body coordinate system in a triaxial way to obtain:
Figure FDA0004083652480000019
wherein [ A ] x A y A z ]Is a distance vector
Figure FDA00040836524800000110
Components projected onto the machine body coordinate system in three axes [ U ] zx U zy U zz ]For the integrated wind speed vector->
Figure FDA00040836524800000111
Components of three-axis projection to body coordinate system, V 1 To the absolute velocity of the projectile, V 0 Airspeed, V, of armed helicopters 01 V is the relative velocity of the projectile w Mu, azimuth of weapon line w The angle is the weapon line height angle, alpha is the transverse entering angle of the armed helicopter, and beta is the longitudinal entering angle of the armed helicopter; phi is the yaw angle of the armed helicopter, theta is the pitch angle of the armed helicopter, and phi is the roll angle of the armed helicopter;
according to (2), the pitch angle mu of the impact point of the projectile c Azimuth v of hit point c And the shot flight time T d The expressions of (2) are respectively:
Figure FDA0004083652480000021
Figure FDA0004083652480000022
Figure FDA0004083652480000023
wherein V is pj Is the average speed of the projectile.
3. The method for analyzing the fire flight coordination mechanism of the armed helicopter based on the multi-target wolf algorithm as set forth in claim 2, wherein the implementation process of the step 2) is as follows:
step 2.1) target aiming angle error analysis:
as is known from (2) - (5), the hit point pitch angle μ c Azimuth v of hit point c Time of flight T of projectile d Yaw angle phi, pitch angle theta, roll angle phi and weapon line height angle mu of armed helicopter w Azimuth v of weapon line w There is a functional relationship:
Figure FDA0004083652480000024
let the target line have a high-low angle mu c c Target line azimuth v c c Then the target aiming angle error equation of the IFFC fire and flight system of the armed helicopter is:
Figure FDA0004083652480000025
wherein N is μ For the error between the high and low angles of the weapon line and the target line, N ν Error of weapon line azimuth and target line azimuth;
to achieve air-to-ground aiming, N μ And N ν Satisfy formula (8):
Figure FDA0004083652480000031
solving (8) to obtain the attitude instruction phi of the armed helicopter in the IFFC fire and flight system c 、θ c 、ψ c And weapon follow-up system command mu w c 、ν w c ；
Let Φ= [ Φθψμ ] w ν w ] T As a parameter vector, a target aiming angle error optimization function is defined:
F 1 (Φ)＝N μ 2 (Φ)+N ν 2 (Φ) (9)
step 2.2) dynamic coupling analysis of target aiming angle errors
IFFC fire and flight systems are divided into two direct coupling channels: { mu c ,μ w θ and { v }, respectively c ,ν w Phi, the rest channels are indirect coupling channels;
through the high and low angles of the target line
Figure FDA0004083652480000032
And target azimuth>
Figure FDA0004083652480000033
For the hit point pitch angle mu c Azimuth v of hit point c And (5) deriving to obtain:
Figure FDA0004083652480000034
on the basis of equation (10), a dynamic coupling matrix G is defined:
Figure FDA0004083652480000035
to determine the effect of an indirect coupling channel on a direct coupling channel, a dynamic coupling function is defined as:
Figure FDA0004083652480000036
based on the formula (12), establishing a coupling influence degree optimization function:
F 2 (Φ)＝K 1 (Φ)+K 2 (Φ) (13)
step 2.3) defining a Multi-objective function optimization model
Defining an air-to-ground aiming multi-target optimization model of a turning turret type weapon of an armed helicopter as follows:
Figure FDA0004083652480000041
wherein phi is max For maximum yaw angle, θ max Is the maximum pitch angle, ψ max At maximum roll angle, mu wmax1 Sum mu wmax2 V is the angle of the maximum weapon line wmax Is the maximum weapon line azimuth.
4. The method for analyzing the fire flight coordination mechanism of the armed helicopter based on the multi-target wolf's nest algorithm according to claim 3, wherein the implementation process of the step 3) is as follows:
step 3.1), the Pareto principle is adopted to measure the solution in the air-to-ground aiming multi-target optimization model of the turning turret weapons of the armed helicopter;
establishing a feasible domain:
Figure FDA0004083652480000042
based on the concept of Pareto optimal solution, the Pareto optimal solution set of the air-to-ground aiming multi-target optimization model of the turning turret type weapon of the armed helicopter is as follows:
Figure FDA0004083652480000043
wherein, the individual solves phi a And phi is b The method comprises the following steps of:
Φ a ＝[φ a ,θ a ,ψ a ,μ wa ,ν wa ] T ∈Ω (17)
Φ b ＝[φ b ,θ b ,ψ b ,μ wb ,ν wb ] T ∈Ω (18)
wherein a and b are parameters;
step 3.2) designing a self-adaptive crowding wolf group individual selection criterion;
the degree of congestion is defined as formula (19):
Figure FDA0004083652480000051
wherein, the individual solves phi i ＝[φ i ,θ i ,ψ i ,μ wi ,ν wi ] T E ρ, i is a parameter, D c (Φ i ) To solve phi for individuals i Degree of congestion, phi i-1 And phi is i+1 Is equal to phi i Adjacent two individual solutions, F m (Φ i+1 ) And F m (Φ i-1 ) To solve phi for individuals i+1 And phi is i+1 The function value of the corresponding mth objective function; f (F) m (Φ max ) And F m (Φ min ) Maximum and minimum values of the mth objective function in the Pareto optimal solution set;
design adaptive congestion degree V (phi) i,t ) As in formula (20):
Figure FDA0004083652480000052
wherein e is an exponential function, t is the iteration number, D c (Φ i,t ) Is the crowding degree, k of the ith individual in the t-th iteration process 1 And k 2 Is an adaptive scaling factor;
design the selection criteria of the wolf and the wolf to be detected:
solving the phi of individual i The definition is as follows:
Figure FDA0004083652480000053
wherein N is w The number of individuals is the number of wolves;
determining the number of individuals of the wolves through the Pareto optimal solution set, and after determining the number of individuals of the wolves, determining the number of the individuals of the Pareto optimal solution set as the probability of being selected as the wolves by using a roulette method is expressed as follows:
Figure FDA0004083652480000054
wherein j is a parameter;
the self-adaptive search direction and step size of the wolf are designed, expressed as:
Figure FDA0004083652480000055
wherein,,
Figure FDA0004083652480000056
for the position of the ith wolf in the d dimension at the t iteration,/th>
Figure FDA0004083652480000057
For the position of the first wolf in the d-th dimension at the t-th iteration, ++>
Figure FDA0004083652480000061
Representing the slash wolf and the head wolf +.>
Figure FDA0004083652480000062
The distance between the two is an exponential function, e is an exponential function, lambda is a logarithmic spiral constant, l 1 Is [ -1,1]Random numbers, k uniformly distributed in interval 3 And k 4 A, b are parameters, which are self-adaptive proportionality coefficients;
the other individual solutions except for the head wolves and the slash wolves are determined as the exploring wolves, and the number of the exploring wolves is S _num The method comprises the steps of carrying out a first treatment on the surface of the The iteration step length and direction of the detection wolf are designed as follows:
Figure FDA0004083652480000063
wherein,,
Figure FDA0004083652480000064
for the j-th detection wolf at the position of the d-th dimension at the t-th iteration,/the position of the j-th detection wolf at the d-th dimension at the t-th iteration>
Figure FDA0004083652480000065
Is the iteration direction, ++>
Figure FDA0004083652480000066
Is the iteration step length, h d Is the number of directions, parameter p d Has a value of 1 to h d ，l 2 Is [0.5,1.5]Random numbers uniformly distributed in the interval;
the implementation process of the multi-target wolf's group algorithm is as follows:
step1: to individual solve phi i Number of individuals N of wolves w Initializing and setting the maximum iteration times t max ；
step2, calculating objective function values of all wolf individuals and determining a Pareto solution set through a Pareto dominance relation;
step3: selecting a first-generation top wolf by definition of adaptive crowding in equation (20) through Pareto optimal solution set established in equation (16)Individuals with a position phi lead The method comprises the steps of carrying out a first treatment on the surface of the The rest individuals in the Pareto optimal solution set select the wolf individuals through a formula (22), and the wolf individuals perform the running behavior through a formula (23); meanwhile, determining a wolf probing individual outside the Pareto optimal solution set, wherein the wolf probing individual walks through a formula (24); when individuals superior to the first wolf are generated in the first wolf individuals and the second wolf individuals, the next step is performed;
step4: updating the Pareto optimal solution set, judging whether the Pareto solution set in step2 reaches an upper limit, if so, eliminating individuals with high crowding degree and carrying out the next step, otherwise, directly carrying out the next step;
step5: judging whether the maximum iteration times t are reached max And outputting all non-inferior solutions in the Pareto solution set in step2 if the solution is reached, otherwise, turning to step2.
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